CamCASP/Programming/4: Difference between revisions
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import>Am592 (→DALTON) |
import>Am592 (→DALTON) |
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I noticed a discrepancy in the e-e and e-n energies (parts of <math>E^{(1)}_{\rm elst}</math>) when calculated in the following ways: |
I noticed a discrepancy in the e-e and e-n energies (parts of <math>E^{(1)}_{\rm elst}</math>) when calculated in the following ways: |
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# MOs calculated in reference geometry and rotated with molecule. |
# MOs calculated in reference geometry and rotated with molecule. DF is done after rotation of MOs. So no integrals needed rotation. |
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# Molecules rotated and MOs calculated in already rotated geometry. |
# Molecules rotated and MOs calculated in already rotated geometry. |
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These should be equivalent. And the MOs should be equivalent and related by a Wigner rotation matrix. This was not the case and I found small, but noticable differences that led to small differences in the e-n energies (there should also be differences in the e-e energies, but I still have to trace other errors here, so cannot be sure). |
These should be equivalent. And the MOs should be equivalent and related by a Wigner rotation matrix. This was not the case and I found small, but noticable differences that led to small differences in the e-n energies (there should also be differences in the e-e energies, but I still have to trace other errors here, so cannot be sure). |
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We should have had the following: |
We should have had the following: |
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# Same e-n energies. But these were -4966220.470061 CM-1 and -4966223.294960 CM-1 for the two methods. The differences are small, but they should not be present. Also, they are small compared with the e-n energy (this was the electrons of the rotated water with the nuclei of the un-rotated partner) but there should be *no* difference! Also, the n-n energy was the same in both cases. So the geometries are identical to a very good precision. |
# Same e-n energies. But these were -4966220.470061 CM-1 and -4966223.294960 CM-1 for the two methods. The differences are small, but they should not be present. Also, they are small compared with the e-n energy (this was the electrons of the rotated water with the nuclei of the un-rotated partner) but there should be *no* difference! Also, the n-n energy was the same in both cases. So the geometries are identical to a very good precision. |
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# |
# All MO coefficients of s-functions should be invariant. These were not. Here are some examples: |
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Rotated MOs: |
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1 2 3 4 5 6 |
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1 -0.41889617 0.09392291 -0.00000000 -0.03428749 -0.00000000 -0.02592316 |
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2 -0.66185094 0.23411329 -0.00000000 -0.08566500 -0.00000000 -0.06621631 |
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3 -0.02169284 -0.49823673 -0.00000000 0.17957929 0.00000000 0.15914437 |
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4 0.01046006 -0.28963061 0.00000000 0.34404529 0.00000000 0.23181807 |
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5 0.01031500 0.20293750 0.00000000 0.25439726 0.00000000 0.23891097 |
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MOs calculated in rotated geometry: |
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1 2 3 4 5 6 |
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1 -0.41889616 0.09392286 0.00000000 0.03428733 0.00000029 0.02592417 |
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2 -0.66185093 0.23411301 0.00000000 0.08566477 0.00000058 0.06621905 |
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3 -0.02169291 -0.49823536 -0.00000000 -0.17958106 0.00000056 -0.15915432 |
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4 0.01046008 -0.28963335 -0.00000000 -0.34402498 -0.00001425 -0.23179758 |
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5 0.01031515 0.20291569 -0.00000000 -0.25431644 -0.00004597 -0.23890003 |
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Columns are MOs and rows are coefficients of primitive AOs. All AOs are s-functions. So all should be the same. But they are not. Also look at MO 5. It should have no s-component. But it does in the second case. So the MOs calculated for the rotated molecule don't seem quite right. |
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Revision as of 16:03, 5 May 2009
CamCASP => Programming => Rotations
The theory of integral and MO rotations has been described in The DF INTEGRAL module . This is a collection of odds and ends related to rotations.
DALTON
MOs from DALTON don't seem to be rotationally invariant. Consider the following example:
water dimer. Sadlej/PBE0/AC MC basis type. Aux basis: JK-tzvpp. Geom: R=2.4 Ang in min-orientation.
I noticed a discrepancy in the e-e and e-n energies (parts of <math>E^{(1)}_{\rm elst}</math>) when calculated in the following ways:
- MOs calculated in reference geometry and rotated with molecule. DF is done after rotation of MOs. So no integrals needed rotation.
- Molecules rotated and MOs calculated in already rotated geometry.
These should be equivalent. And the MOs should be equivalent and related by a Wigner rotation matrix. This was not the case and I found small, but noticable differences that led to small differences in the e-n energies (there should also be differences in the e-e energies, but I still have to trace other errors here, so cannot be sure).
We should have had the following:
- Same e-n energies. But these were -4966220.470061 CM-1 and -4966223.294960 CM-1 for the two methods. The differences are small, but they should not be present. Also, they are small compared with the e-n energy (this was the electrons of the rotated water with the nuclei of the un-rotated partner) but there should be *no* difference! Also, the n-n energy was the same in both cases. So the geometries are identical to a very good precision.
- All MO coefficients of s-functions should be invariant. These were not. Here are some examples:
Rotated MOs:
1 2 3 4 5 6 1 -0.41889617 0.09392291 -0.00000000 -0.03428749 -0.00000000 -0.02592316 2 -0.66185094 0.23411329 -0.00000000 -0.08566500 -0.00000000 -0.06621631 3 -0.02169284 -0.49823673 -0.00000000 0.17957929 0.00000000 0.15914437 4 0.01046006 -0.28963061 0.00000000 0.34404529 0.00000000 0.23181807 5 0.01031500 0.20293750 0.00000000 0.25439726 0.00000000 0.23891097
MOs calculated in rotated geometry:
1 2 3 4 5 6 1 -0.41889616 0.09392286 0.00000000 0.03428733 0.00000029 0.02592417 2 -0.66185093 0.23411301 0.00000000 0.08566477 0.00000058 0.06621905 3 -0.02169291 -0.49823536 -0.00000000 -0.17958106 0.00000056 -0.15915432 4 0.01046008 -0.28963335 -0.00000000 -0.34402498 -0.00001425 -0.23179758 5 0.01031515 0.20291569 -0.00000000 -0.25431644 -0.00004597 -0.23890003
Columns are MOs and rows are coefficients of primitive AOs. All AOs are s-functions. So all should be the same. But they are not. Also look at MO 5. It should have no s-component. But it does in the second case. So the MOs calculated for the rotated molecule don't seem quite right.